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/*
-- MAGMA (version 2.9.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2025
@generated from testing/testing_zhesv.cpp, normal z -> d, Wed Jan 22 14:40:28 2025
@author Ichitaro Yamazaki
*/
// includes, system
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>
// includes, project
#include "flops.h"
#include "magma_v2.h"
#include "magma_lapack.h"
#include "testings.h"
/* ================================================================================================== */
// Initialize matrix to random.
// This ensures the same ISEED is always used,
// so we can re-generate the identical matrix.
void init_matrix(
magma_opts &opts,
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda )
{
magma_int_t iseed_save[4];
for (magma_int_t i = 0; i < 4; ++i) {
iseed_save[i] = opts.iseed[i];
}
magma_generate_matrix( opts, m, n, A, lda );
// restore iseed
for (magma_int_t i = 0; i < 4; ++i) {
opts.iseed[i] = iseed_save[i];
}
}
// On input, A and ipiv is LU factorization of A. On output, A is overwritten.
// Requires m == n.
// Uses init_matrix() to re-generate original A as needed.
// Generates random RHS b and solves Ax=b.
// Returns residual, |Ax - b| / (n |A| |x|).
double get_residual(
magma_opts &opts,
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
double *A, magma_int_t lda, magma_int_t *ipiv,
double *x, magma_int_t ldx,
double *b, magma_int_t ldb)
{
const double c_one = MAGMA_D_ONE;
const double c_neg_one = MAGMA_D_NEG_ONE;
const magma_int_t ione = 1;
// reset to original A
init_matrix( opts, n, n, A, lda );
// compute r = Ax - b, saved in b
blasf77_dsymv( lapack_uplo_const(uplo), &n, &c_one, A, &lda, x, &ione, &c_neg_one, b, &ione );
// compute residual |Ax - b| / (n*|A|*|x|)
double norm_x, norm_A, norm_r, work[1];
norm_A = lapackf77_dlansy( "Fro", lapack_uplo_const(uplo), &n, A, &lda, work );
norm_r = lapackf77_dlange( "Fro", &n, &ione, b, &n, work );
norm_x = lapackf77_dlange( "Fro", &n, &ione, x, &n, work );
//printf( "r=\n" ); magma_dprint( 1, n, b, 1 );
//printf( "r=%.2e, A=%.2e, x=%.2e, n=%lld\n", norm_r, norm_A, norm_x, (long long) n );
return norm_r / (n * norm_A * norm_x);
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dsysv
*/
int main( int argc, char** argv)
{
TESTING_CHECK( magma_init() );
magma_print_environment();
double *h_A, *h_B, *h_X, *work, temp;
real_Double_t gflops, gpu_perf, gpu_time = 0.0, cpu_perf=0, cpu_time=0;
double error, error_lapack = 0.0;
magma_int_t *ipiv;
magma_int_t N, n2, lda, ldb, sizeB, lwork, info;
magma_int_t ione = 1;
magma_int_t ISEED[4] = {0,0,0,1};
int status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
double tol = opts.tolerance * lapackf77_dlamch("E");
printf("%% M N CPU Gflop/s (sec) GPU Gflop/s (sec) |Ax-b|/(N*|A|*|x|)\n");
printf("%%========================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
ldb = N;
lda = N;
n2 = lda*N;
sizeB = ldb*opts.nrhs;
gflops = ( FLOPS_DPOTRF( N ) + FLOPS_DPOTRS( N, opts.nrhs ) ) / 1e9;
TESTING_CHECK( magma_imalloc_cpu( &ipiv, N ));
TESTING_CHECK( magma_dmalloc_pinned( &h_A, n2 ));
TESTING_CHECK( magma_dmalloc_pinned( &h_B, sizeB ));
TESTING_CHECK( magma_dmalloc_pinned( &h_X, sizeB ));
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.lapack ) {
lwork = -1;
lapackf77_dsysv(lapack_uplo_const(opts.uplo), &N, &opts.nrhs,
h_A, &lda, ipiv, h_X, &ldb, &temp, &lwork, &info);
lwork = (magma_int_t)MAGMA_D_REAL(temp);
TESTING_CHECK( magma_dmalloc_cpu( &work, lwork ));
init_matrix( opts, N, N, h_A, lda );
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_dlacpy( MagmaFullStr, &N, &opts.nrhs, h_B, &ldb, h_X, &ldb );
cpu_time = magma_wtime();
lapackf77_dsysv(lapack_uplo_const(opts.uplo), &N, &opts.nrhs,
h_A, &lda, ipiv, h_X, &ldb, work, &lwork, &info);
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_dsysv returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
error_lapack = get_residual( opts, opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, h_B, ldb );
magma_free_cpu( work );
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
init_matrix( opts, N, N, h_A, lda );
lapackf77_dlarnv( &ione, ISEED, &sizeB, h_B );
lapackf77_dlacpy( MagmaFullStr, &N, &opts.nrhs, h_B, &ldb, h_X, &ldb );
magma_setdevice(0);
gpu_time = magma_wtime();
magma_dsysv( opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, &info);
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_dsysv returned error %lld: %s.\n",
(long long) info, magma_strerror( info ));
}
/* =====================================================================
Check the factorization
=================================================================== */
if ( opts.lapack ) {
printf("%5lld %5lld %7.2f (%7.2f) %7.2f (%7.2f)",
(long long) N, (long long) N, cpu_perf, cpu_time, gpu_perf, gpu_time );
}
else {
printf("%5lld %5lld --- ( --- ) %7.2f (%7.2f)",
(long long) N, (long long) N, gpu_perf, gpu_time );
}
if ( opts.check == 0 ) {
printf(" --- \n");
} else {
error = get_residual( opts, opts.uplo, N, opts.nrhs, h_A, lda, ipiv, h_X, ldb, h_B, ldb );
printf(" %8.2e %s", error, (error < tol ? "ok" : "failed"));
if (opts.lapack)
printf(" (lapack rel.res. = %8.2e)", error_lapack);
printf("\n");
status += ! (error < tol);
}
magma_free_cpu( ipiv );
magma_free_pinned( h_X );
magma_free_pinned( h_B );
magma_free_pinned( h_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_CHECK( magma_finalize() );
return status;
}
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